| Date | May 2010 | Marks available | 2 | Reference code | 10M.1.sl.TZ1.5 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Write down | Question number | 5 | Adapted from | N/A |
Question
The volume of a sphere is \(V{\text{ = }}\sqrt {\frac{{{S^3}}}{{36\pi }}} \), where \(S\) is its surface area.
The surface area of a sphere is 500 cm2 .
Calculate the volume of the sphere. Give your answer correct to two decimal places.
Write down your answer to (a) correct to the nearest integer.
Write down your answer to (b) in the form \(a \times {10^n}\), where \(1 \leqslant a < 10\) and \(n \in \mathbb{Z}\).
Markscheme
\(V{\text{ = }}\sqrt {\frac{{{500^3}}}{{36\pi }}} \) (M1)
Note: Award (M1) correct substitution into formula.
V = 1051.305 … (A1)
V = 1051.31 cm3 (A1)(ft) (C3)
Note: Award last (A1)(ft) for correct rounding to 2 decimal places of their answer. Unrounded answer must be seen so that the follow through can be awarded.
[3 marks]
1051 (A1)(ft)
[1 mark]
\(1.051 \times {10^3}\) (A1)(ft)(A1)(ft) (C2)
Note: Award (A1) for 1.051 (accept 1.05) (A1) for \( \times {10^3}\).
[2 marks]
Examiners report
This question was well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.
This question was well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part (a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.
This question was well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.
